Answer :
To determine which fractions satisfy the inequality [tex]\(\frac{6}{10} > \frac{1}{3}\)[/tex], we need to compare each option to [tex]\(\frac{1}{3}\)[/tex].
Let's check each option step by step:
1. Option A: [tex]\(\frac{1}{2}\)[/tex]
- Compare [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{2} = 0.5 \quad \text{and} \quad \frac{1}{3} \approx 0.333 \][/tex]
Since [tex]\(0.5 > 0.333\)[/tex], [tex]\(\frac{1}{2} > \frac{1}{3}\)[/tex].
2. Option B: [tex]\(\frac{1}{4}\)[/tex]
- Compare [tex]\(\frac{1}{4}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{4} = 0.25 \quad \text{and} \quad \frac{1}{3} \approx 0.333 \][/tex]
Since [tex]\(0.25 < 0.333\)[/tex], [tex]\(\frac{1}{4} < \frac{1}{3}\)[/tex].
3. Option C: [tex]\(\frac{2}{3}\)[/tex]
- Compare [tex]\(\frac{2}{3}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{2}{3} \approx 0.667 \quad \text{and} \quad \frac{1}{3} \approx 0.333 \][/tex]
Since [tex]\(0.667 > 0.333\)[/tex], [tex]\(\frac{2}{3} > \frac{1}{3}\)[/tex].
4. Option D: [tex]\(\frac{3}{4}\)[/tex]
- Compare [tex]\(\frac{3}{4}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{3}{4} = 0.75 \quad \text{and} \quad \frac{1}{3} \approx 0.333 \][/tex]
Since [tex]\(0.75 > 0.333\)[/tex], [tex]\(\frac{3}{4} > \frac{1}{3}\)[/tex].
Based on these comparisons, the fractions that are greater than [tex]\(\frac{1}{3}\)[/tex] are Option A [tex]\(\frac{1}{2}\)[/tex], Option C [tex]\(\frac{2}{3}\)[/tex], and Option D [tex]\(\frac{3}{4}\)[/tex]. These correspond to:
- A [tex]\(\frac{1}{2}\)[/tex]
- C [tex]\(\frac{2}{3}\)[/tex]
- D [tex]\(\frac{3}{4}\)[/tex]
Therefore, the correct choices are:
A, C, and D or numerically, [1, 3, and 4].
Let's check each option step by step:
1. Option A: [tex]\(\frac{1}{2}\)[/tex]
- Compare [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{2} = 0.5 \quad \text{and} \quad \frac{1}{3} \approx 0.333 \][/tex]
Since [tex]\(0.5 > 0.333\)[/tex], [tex]\(\frac{1}{2} > \frac{1}{3}\)[/tex].
2. Option B: [tex]\(\frac{1}{4}\)[/tex]
- Compare [tex]\(\frac{1}{4}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{4} = 0.25 \quad \text{and} \quad \frac{1}{3} \approx 0.333 \][/tex]
Since [tex]\(0.25 < 0.333\)[/tex], [tex]\(\frac{1}{4} < \frac{1}{3}\)[/tex].
3. Option C: [tex]\(\frac{2}{3}\)[/tex]
- Compare [tex]\(\frac{2}{3}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{2}{3} \approx 0.667 \quad \text{and} \quad \frac{1}{3} \approx 0.333 \][/tex]
Since [tex]\(0.667 > 0.333\)[/tex], [tex]\(\frac{2}{3} > \frac{1}{3}\)[/tex].
4. Option D: [tex]\(\frac{3}{4}\)[/tex]
- Compare [tex]\(\frac{3}{4}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{3}{4} = 0.75 \quad \text{and} \quad \frac{1}{3} \approx 0.333 \][/tex]
Since [tex]\(0.75 > 0.333\)[/tex], [tex]\(\frac{3}{4} > \frac{1}{3}\)[/tex].
Based on these comparisons, the fractions that are greater than [tex]\(\frac{1}{3}\)[/tex] are Option A [tex]\(\frac{1}{2}\)[/tex], Option C [tex]\(\frac{2}{3}\)[/tex], and Option D [tex]\(\frac{3}{4}\)[/tex]. These correspond to:
- A [tex]\(\frac{1}{2}\)[/tex]
- C [tex]\(\frac{2}{3}\)[/tex]
- D [tex]\(\frac{3}{4}\)[/tex]
Therefore, the correct choices are:
A, C, and D or numerically, [1, 3, and 4].
